Datasheet

LTC3816
19
3816f
applicaTions inForMaTion
achieve accurate current sensing. Figure 4 shows a real
current sensing resistor, R
SENSE
, which can be modeled
with an ideal resistance, R
SEN
, in series with its parasitic
ESL. As shown in Figure 4, the voltage across the sense
resistor includes the voltage across the parasitic induc-
tor which is a strong function of inductor ripple current
and the switching frequency. This effectively reduces the
current limit threshold, typically by more than 30%. The
voltage across the sense resistor can be extracted from
a lowpass filter placed close to the controller input sense
pins as shown in Figure 4. The voltage across the sensing
capacitor, C
ISR
, is:
V I R
sESL
R
sR C
CISR L SEN
SEN
ISR ISR
=
+
+








•
•
1
1




In the frequency domain, the second term in the above
equation must be equal to 1 to ensure that the voltage
across the filter capacitor is independent of operating
frequency. To meet this requirement, the value of the RC
filter should fulfill the following condition:
R C
ESL
R
ISR ISR
SEN
• =
The ESL value can be obtained from the manufacturer ’s
data sheet or estimated with an oscilloscope, as shown in
the Figure 4 waveform, using the following equation:
ESL
V V
I
t t
ESL ON ESL OFF
L
ON OFF
=
+
+






( ) ( )
∆
1 1
where t
ON
is the TG on time and t
OFF
is the TG off time.
For high efficiency applications, the inductor DCR provides
a method of sensing the inductor current without incurring
additional power loss from a sense resistor. The DCR of
the inductor represents the small amount of resistance
in the copper winding, which can be less than 1mΩ for
today
’
s low value, high current inductors. Figure 5 shows
a simplified inductor model, which can be modeled with an
ideal inductor, L, in series with its parasitic DCR. The DCR
value can be obtained from the inductor manufacturer ’s
data sheet. Similar to the sense resistor application circuit,
the voltage across the inductor DCR can be extracted from
a lowpass filter and the current limit threshold is given by
the following equation:
I
I R
R
I I I
L PEAK
IMAX IMAX
DCR
LOAD MAX LIMIT L PE
( )
( ) (
•
=
< =
AAK
L IMAX IMAX
DCR
L
IDCR IDCR
I I R
R
I
if R C
L
R
)
–
•
–
•
∆ ∆
2 2
=
=
DDCR
+
Q
B
D
L
Q
T
V
IN
ESL
C
OUT
V
OUT
I
L
SENSE RESISTOR
R
SEN
R
ISR
V
ISR
R
IMAX
C
ISR
TG
BG
BSOURCE
I
SENP
I
SENN
I
MAX
LTC3816
SW
V
ESL(OFF)
V
ESL(ON)
3816 F04
V
ISR
= V
RSEN
+ V
ESL
V
RSEN
= I
L
• R
SEN
Figure 4. Current Limit Sensing Using
a Low Value Sense Resistor
+
Q
B
D
Q
T
V
IN
L
C
OUT
3916 F05
V
OUT
I
L
INDUCTOR
DCR
R
IDCR
R
IMAX
C
IDCR
TG
BG
BSOURCE
I
SENP
I
SENN
I
MAX
LTC3816
SW
Figure 5. Current Limit Sensing Using Inductor DCR